A conductor ABC has AB=ℓ₁ parallel to the x-axis and BC=ℓ₂ parallel to the y-axis. It moves with velocity v⃗=vₓî+vᵧĵ in a uniform magnetic field B normal to the xy-plane. The potential difference between A and C is proportional to:

Question

G1 Physics · Accepted Answer

Using ε=∫(v⃗×B⃗)·dℓ⃗, the contributions of AB and BC have opposite signs and are proportional to vᵧℓ₁ and vₓℓ₂. Thus the required expression is proportional to vₓℓ₂-vᵧℓ₁.